Making a Difference

Help students learn from each other
. Create opportunities for students 
to teach each other, to summarize main points, and to tutor each other in new 
concepts in short (e.g., 
fi
ve-minute) tutoring sessions. These types of collaborative 
activities can enhance student motivation to learn mathematics as well as create 
opportunities to learn about working with others.
Help students be independent
. Effective scaffolding involves listening and 
watching for clues from students as to when teacher assistance is or is not needed. 
Achieving independence is different for individual students. Some students 
may be at identical skill levels, but emotionally they may be at different levels 
regarding the amount of frustration they can tolerate. Some students will need 
more teacher support while learning to perform a task; others will demonstrate 
task mastery more quickly.
Consider the following examples of scaffolding that create choice and provide 
structured opportunities to re
fl
ect on mathematical learning.
Open-ended problem solving
Learning through problem solving needs to be the focus of mathematics at all 
grade levels. In a problem-solving classroom, problems are used as a vehicle to 
learn new mathematics.
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One way to create this is to use open-ended tasks that provide multiple entry 
points for students at varying readiness levels. For example,
The answer is 12, what is the question?
Broken calculator activities are also open-ended. For example,
Suppose the only working keys are [3] [8] [x] [–] [=].
Show how you can still get all the answers from 1 to 10. 
• 
What is the least number of key strokes (button presses) it takes to get 
• 
each one?